The problem of discovering frequent itemsets including rare ones has received a great deal of attention. The mining process needs to be flexible enough to extract frequent and rare regularities at once. On the other hand, it has recently been shown that constraint programming is a flexible way to tackle data mining tasks. In this paper, we propose a constraint programming approach for mining itemsets with multiple minimum supports. Our approach provides the user with the possibility to express any kind of constraints on the minimum item supports. An experimental analysis shows the practical effectiveness of our approach compared to the state of the art.